# Euler's method Calculator

## Calculates the solution y=f(x) of the linear ordinary differential equation y'=F(x,y) using Euler's method.

 The initial condition is y0=f(x0), and the root x is calculated within the range of from x0 to xn. $\normal \\\vspace{10}y'=F(x,y)\hspace{30} y_0=f(x_0)\rightarrow\ y=f(x)\\$
F(x,y)
x0
 initial condition
y0
 = f(x0)
xn
 x0≦x≦xn
 [ partition n 10 20 50 100 200 500 ]
 6dgt10dgt14dgt18dgt22dgt26dgt30dgt34dgt38dgt42dgt46dgt50dgt
 $\normal Euler's\ method\\[10pt](1)\ y'=F(x,y),\hspace{30} y_0=f(x_0)\rightarrow\ y=f(x)\\(2)\ y_{n+1}=y_n+hF(x_n,\ y_n)+{\small O}(h^2), \hspace{5} x_n=x_0+nh\\$

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